Suppose f (x,y) = x y , P = (1,−4) and v = −2i+4j. A. Find the gradient of f. Ñf = i+ j Note: Your answers should be expressions of x and y; e.g. “3x - 4y” B. Find the gradient of f at the point P. (Ñf ) (P) = i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Du f = Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u = i+ j Note: Your answers should be numbers Answer(s) submitted: •

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Suppose f (x,y) = x y , P = (1,−4) and v = −2i+4j. A. Find the gradient of f. Ñf = i+ j Note: Your answers should be expressions of x and y; e.g. “3x - 4y” B. Find the gradient of f at the point P. (Ñf ) (P) = i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Du f = Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u = i+ j Note: Your answers should be numbers Answer(s) submitted: •

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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